Autoregressive decoding relies on the KV cache, whose memory footprint grows linearly with context length and caps batch size and throughput. Existing post-training methods exploit redundancy across tokens, layers, and feature dimensions, or lower numerical precision. We identify a complementary axis: within each attention head, values are largely predictable from their corresponding keys. We exploit this with value cache amortisation, which fits a lightweight per-head predictor at test time and stores residuals only for the tokens it reconstructs worst, giving $4\times$ near-lossless value compression. The predictor can be initialised by meta-learning for substantially reduced prefill overhead, or fitted from scratch in settings that allow a one-off cost, such as multi-query inference. We pair value amortisation with cross-layer low-rank key compression to produce LowRAM, an asymmetric compression pipeline that stays close to lossless across three model families. By reconstructing only a selected subset of KV pairs at each decoding step, LowRAM can keep decoding overhead minimal and achieve up to $5\times$ higher peak decode throughput at $4\times$ compression. LowRAM further composes with quantisation and eviction, reaching $26.9\times$ compression at $94.5\%$ of baseline performance on long contexts. These results show that treating keys and values as structurally distinct enables efficient, aggressive, and composable KV cache compression.

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